Chapter 6.3, Problem 83E

a.

To determine

To explain: The reason of X being a binomial random variable

Explanation of Solution

Given:

Number of trials ( n ) = 12

Probability of success ( p ) = 0.80

Following requiremens are fulfilled by the random variable X .

1. Probability of success, that is, probability that the spinner will land in the blue region ( p ) which is equal to 0.80 is fixed.
2. Number of time spinner is spin is fixed.
3. Spins are independent of each other.
4. There are two outcomes, that is spinner lands in the blue region and it does not land in the blue region

All the binomial conditions are fullfilled here. Thus, it could be said that X follows the binomial distribution

b.

To determine

To find: The probability that 8 spins land in the blue region.

Answer to Problem 83E

The probability is 0.1329.

Explanation of Solution

The probability that 8 spins land in the blue region can be calculated as:

  $\begin{array}{c}P\left(X=8\right){=}^{12}{C}_8\times {\left(0.80\right)}^8\times {\left(1-0.80\right)}^{12-8}\\ =0.1329\end{array}$

Thus, the required probability is 0.1329.